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On Randić spectrum of zero divisor graphs of commutative ring $\mathbb{Z}_{n} $ | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 8، دوره 8، شماره 1، خرداد 2023، صفحه 103-113 اصل مقاله (487.63 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2021.27202.1212 | ||
| نویسندگان | ||
| Bilal Rather1؛ Shariefuddin Pirzada* 2؛ Imran Bhat3؛ Tariq Chishti1 | ||
| 1University of Kashmir | ||
| 2Department of Mathematics, Hazratbal | ||
| 3Central University of Kashmir | ||
| چکیده | ||
| For a finite commutative ring $ \mathbb{Z}_{n} $ with identity $ 1\neq 0 $, the zero divisor graph $ \Gamma(\mathbb{Z}_{n}) $ is a simple connected graph having vertex set as the set of non-zero zero divisors, where two vertices $ x $ and $ y $ are adjacent if and only if $ xy=0 $. We find the Randi'c spectrum of the zero divisor graphs $ \Gamma(\mathbb{Z}_{n}) $, for various values of $ n$ and characterize $ n $ for which $ \Gamma(\mathbb{Z}_{n}) $ is Randi'c integral. | ||
| کلیدواژه‌ها | ||
| Randić matrix؛ Randić spectrum؛ zero divisor graph؛ commutative rings | ||
| مراجع | ||
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[1] D.D. Anderson and M. Naseer, Beck’s coloring of a commutative ring, J. Algebra 159 (1993), no. 2, 500–514.
[2] D.F. Anderson and P.S. Livingston, The zero-divisor graph of a commutative ring, J. Algebra 217 (1999), no. 2, 434–447.
[3] E. Andrade, H. Gomes, and M. Robbiano, Spectra and Randić spectra of caterpillar graphs and applications to the energy, MATCH Commun. Math. Comput. Chem. 77 (2017), no. 1, 61–75.
[4] S. Bozkurt, A. Güngör, I. Gutman, and A.S. Cevik, Randić matrix and Randić energy, MATCH Commun. Math. Comput. Chem. 64 (2010), no. 1, 239–250.
[5] D.M. Cardoso, M.A.A. de Freitas, E. Andrade Martins, and M. Robbiano, Spectra of graphs obtained by a generalization of the join graph operation, Discrete Math. 313 (2013), no. 5, 733–741.
[6] S. Chattopadhyay, K.L. Patra, and B.K. Sahoo, Laplacian eigenvalues of the zero divisor graph of the ring Zn , Linear Algebra Appl. 584 (2020), 267–286.
7] D.M. Cvetković, P. Rowlison, and S. Simić, An Introduction to Theory of Graph Spectra, Lon. Math. Society Student Text, 75. Cambridge University Press, Inc. UK, 2010.
[8] Z. Du, A. Jahanbai, and S.M. Sheikholeslami, Relationships between Randić index and other topological indices, Commun. Comb. Optim. 6 (2021), no. 1, 137–154.
[9] R. Horn and C. Johnson, Matrix Analysis, Cambridge University Press, 1985.
[10] S. Pirzada, An Introduction to Graph Theory, Universities Press, Orient BlackSwan, Hyderabad, 2012.
[11] S. Pirzada, B.A. Rather, M. Aijaz, and T.A. Chishti, On distance signless Laplacian spectrum of graphs and spectrum of zero divisor graphs of Zn, Linear Multilinear Algebra (2020), in press.
[12] S. Pirzada, B.A. Rather, and T.A. Chishti, On distance Laplacian spectrum of zero divisor graphs of the ring Zn, Carpathian Math. Publ. 13 (2021), no. 1, 48–57.
[13] S. Pirzada, B.A. Rather, T.A. Chishti, and U. Samee, On normalized Laplacian spectrum of zero divisor graphs of commutative ring Zn, Electronic J. Graph Theory Appl. 9 (2021), no. 2, 331–345.
[14] S. Pirzada, B.A. Rather, R.U.l. Shaban, and M.I. Bhat, On distance Laplacian (signless) eigenvalues of commuting graphs of dihedral and dicyclic groups, Springer Proceedings on Algebra and Related Topics with Applications.
[15] S. Pirzada, B.A. Rather, R.U.l. Shaban, and S. Merajuddin, On signless Laplacian spectrum of the zero divisor graphs of the ring Zn, Korean J. Math. 29 (2021), no. 1, 13–24.
[16] S. Pirzada, B.A. Wani, and A. Somasundaram, On the eigenvalues of zero-divisor graph associated to finite commutative ring ZpMqN , AKCE Int. J. Graphs Comb. 18 (2021), no. 1, 1–16.
[17] B.A. Rather, S. Pirzada, T.A. Naikoo, and Y. Shang, On Laplacian eigenvalues of the zero-divisor graph associated to the ring of integers modulo n, Mathematics 9 (2021), no. 5, ID: 482.
[18] B.-F. Wu, Y.-Y. Lou, and C.-X. He, Signless Laplacian and normalized Laplacian on the h-join operation of graphs, Discrete Math. Algorithms Appl. 6 (2014), no. 3, ID: 1450046.
[19] M. Young, Adjacency matrices of zero-divisor graphs of integers modulo n, Involve 8 (2015), no. 5, 753–761. | ||
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